Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Consider the linear parabolic operator in divergence form $$\mathcal{H} u =\partial_t u(X,t)-\text{div}(A(X)\nabla u(X,t)).$$ We employ a method of Dahlberg to show that the Dirichlet problem for $\mathcal{H}$ in the upper half plane is well-posed for boundary data in $L^p$, for any elliptic matrix of coefficients $A$ which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation $\partial_t u_\varepsilon(X,t)-\text{div}(A(X/\varepsilon)\nabla u_\varepsilon(X,t))$ in Lipschitz domains with $L^p$-boundary data.Comment: 21 page

On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are admitted). Our investigations include maximal operators, $g$-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes transform type. Using the general Calder\'on-Zygmund theory we prove that these objects are bounded in weighted $L^p$ spaces, $1<p<\infty$, and from $L^1$ into weak $L^{1}$.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1011.3615 by other author

Calder\'on-Zygmund operators in the Bessel setting for all possible type indices

In this paper we adapt the technique developed in [17] to show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, Calder\'on-Zygmund operators for all possible values of type parameter $\lambda$ in this context. This extends the results obtained recently in [7], which are valid only for a restricted range of $\lambda$.Comment: 12 page

Bounds for partial derivatives: necessity of UMD and sharp constants

We prove the necessity of the UMD condition, with a quantitative estimate of the UMD constant, for any inequality in a family of $L^p$ bounds between different partial derivatives $\partial^\beta u$ of $u\in C^\infty_c(\mathbb{R}^n,X)$. In particular, we show that the estimate $\|u_{xy}\|_p\leq K(\|u_{xx}\|_p+\|u_{yy}\|_p)$ characterizes the UMD property, and the best constant $K$ is equal to one half of the UMD constant. This precise value of $K$ seems to be new even for scalar-valued functions.Comment: v2: corrected typo in the reference

La mirada latina sobre la psicología positiva

El siguiente trabajo intenta mostrar el avance que presenta Latinoamérica en cuanto al estudio y aplicación de temáticas relacionadas con la Psicología Positiva (PP). Por un lado, se pretendió describir cómo ha surgido el interés en PP en algunos países de Latinoamérica como Argentina, Perú, México, entre otros. Por otro lado, se analizaron los resultados de un rastrillaje realizado en el cual verifica el cúmulo de trabajos y pruebas psicológicas desarrolladas en la región, principalmente teniendo en cuenta los pilares de la PP propuestos por Seligman (2002, 2009): las emociones positivas, los rasgos positivos, las instituciones positivas y los vínculos positivos (la vida social). México, Chile, Brasil y Argentina, parecen ser los países con mayor productividad. Las temáticas frecuentemente estudiadas están en relación con el bienestar psicológico, las relaciones interpersonales y las intervenciones psicoterapéuticas. Palabras clave: Psicología positiva, pilares, evaluación, Latinoamérica.The present article aims to describe the progress of the study and application of Positive Psychology (PP) in Latin America. On one hand, it is described how the interest in PP has emerged in some Latin American countries such as Argentina, Peru and Mexico, among others. On the other hand, results of a literature review which explore the development of psychological assessments in the region are presented according to PP pillars proposed by Seligman (2002, 2009): positive emotions, positive traits, positive institutions and positive relationships (social life). Mexico, Chile, Brazil and Argentina appeared to be the countries with the highest levels of scientific production related to PP and the topics most frequently studied are psychological well-being, interpersonal relationships and psychotherapeutic interventions.Fil: Castro Solano, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Palermo; ArgentinaFil: Lupano Perugini, Maria Laura. Universidad de Palermo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

“La víctima en el sistema penal mexicano”

A manera de conjeturas podemos establecer que, la víctima constituye un eje rector dentro todo sistema penal, pues el delito es una situación de hecho en el cual inciden factores sociales, económicos, políticos, fiscales, etc., que aportarán los elementos que deben tomarse en cuenta en consideración para la construcción por parte del legislador de los tipos, pero dichas circunstancias no significa que necesariamente deban recibir la denominación a partir de algún o alguno de los elementos que contenga, ya que con ello resulta afectación la víctima.La presente investigación se desarrollará dentro del ámbito espacial del Estado de México, con la intención de estudiar el fenómeno de las vulneraciones de los bienes jurídicos tutelados por el Estado. Para establecer el lugar y tiempo de estudio, que se encuentran relacionados, nos delimitaremos a estudiar la reforma constitucional publicada en el Diario Oficial de la Federación del 18 de junio del 2008 a diciembre de 2015; por lo que la justificación de la fecha y lugar del objeto de estudio se sustenta en aquel lugar y tiempo, ya que esta reforma crea un nuevo paradigma constitucional, donde la victima forma parte dentro de los sujetos procesales.

Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with H\"older continuous coefficients

We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is achieved through the demonstration of invertibility of the relevant layer-potentials which is in turn based on Fredholm theory and a new systematic approach which yields suitable parabolic Rellich-type estimates

Calder\'on-Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.Comment: 21 page

Transference of local to global L2L^2 maximal estimates for dispersive partial differential equations

In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local $L^2$ estimates for certain oscillatory integrals with rough phase functions, to the corresponding global estimates. The elementary feature of our approach is that it entirely avoids the use of the wave packet techniques which are quite common in this context, and instead is based on scalings and classical oscillatory integral estimates.Comment: 10 page

UMD Banach spaces and the maximal regularity for the square root of several operators

In this paper we prove that the maximal $L^p$-regularity property on the interval $(0,T)$, $T>0$, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on $L^2(\Omega, d\mu; X),$ characterizes the UMD property for the Banach space $X$.Comment: 23 pages. To appear in Semigroup Foru